Reallocation of excess power for full channel-state information (CSI) multiple-input, multiple-output (MIMO) systems

ABSTRACT

Techniques to allocate the total transmit power to the transmission channels in a multi-channel communication system such that higher overall system spectral efficiency and/or other benefits may be achieved. The total transmit power may be initially allocated to the transmission channels based on a particular power allocation scheme (e.g., the water-filling scheme). The initial allocation may result in more power being allocated to some transmission channels than needed to achieve the required SNR (e.g., the SNR needed to achieve the maximum allowed data rate), which would then result in these transmission channels being operated in the saturation region. In such situations, the techniques reallocate the excess transmit power of transmission channels operated in the saturation region to other transmission channels operated below the saturation region. In this way, higher data rate may be achieved for the “poorer” transmission channels without sacrificing the performance of the “better” transmission channels.

CLAIM OF PRIORITY UNDER 35 U.S.C. §120

The present Application for Patent is a Continuation inPart/Continuation and claims priority to patent application Ser. No.10/056,275 entitled “Reallocation of Excess Power for Full Channel-StateInformation (CSI) Multiple-Input, Multiple-Output (MIMO) Systems” filedJan. 23, 2002, now allowed, and assigned to the assignee hereof andhereby expressly incorporated by reference herein.

BACKGROUND

1. Field

The present invention relates generally to data communication, and morespecifically to techniques for reallocating excess power in amulti-channel communication system (e.g., a multiple-input,multiple-output (MIMO) communication system).

2. Background

In a wireless communication system, an RF modulated signal from atransmitter may reach a receiver via a number of propagation paths. Thecharacteristics of the propagation paths typically vary over time due toa number of factors such as fading and multipath. To provide diversityagainst deleterious path effects and improve performance, multipletransmit and receive antennas may be used. If the propagation pathsbetween the transmit and receive antennas are linearly independent(i.e., a transmission on one path is not formed as a linear combinationof the transmissions on other paths), which is generally true to atleast an extent, then the likelihood of correctly receiving a datatransmission increases as the number of antennas increases. Generally,diversity increases and performance improves as the number of transmitand receive antennas increases.

A multiple-input, multiple-output (MIMO) communication system employsmultiple (N_(T)) transmit antennas and multiple (N_(R)) receive antennasfor data transmission. A MIMO channel formed by the N_(T) transmit andN_(R) receive antennas may be decomposed into N_(S) independentchannels, with N_(S)≦min {N_(T), N_(R)}. Each of the N_(S) independentchannels is also referred to as a spatial subchannel of the MIMO channeland corresponds to a dimension. The MIMO system can provide improvedperformance (e.g., increased transmission capacity) if the additionaldimensionalities created by the multiple transmit and receive antennasare utilized. For example, an independent data stream may be transmittedon each of the N_(S) spatial subchannels to increase system throughput.

The spatial subchannels of a wideband MIMO system may experiencedifferent channel conditions (e.g., different fading and multipatheffects) and may achieve different signal-to-noise ratios (SNRs) for agiven amount of transmit power. Consequently, the data rates that may besupported by the spatial subchannels may be different from subchannel tosubchannel. Moreover, the channel conditions typically vary with time.As a result, the data rates supported by the spatial subchannels alsovary with time.

A key challenge in a coded communication system is the selection of theappropriate data rates, coding and modulation schemes, and transmitpowers to be used for data transmission on the available transmissionchannels based on the channel conditions. The goal of this selectionprocess should be to maximize spectral efficiency while meeting qualityobjectives, which may be quantified by a particular target frame errorrate (FER) and/or some other criteria.

In a typical communication system, there may be an upper limit on thedata rate that may be used for any given data stream. For example, a setof discrete data rates may be supported by the system, and the maximumdata rate from among these discrete data rates may be considered as thesaturation spectral efficiency, ρ_(sat), for any given data stream. Insuch a system, if each data stream is transmitted on a respectivespatial subchannel, then allocating more transmit power than necessaryto achieve the target FER at the maximum data rate would result in anineffective use of the additional transmit power. Even though the excesstransmit power may result in a lower FER, this improvement in FER maynot be considered substantial since the target FER has already beenachieved. The excess transmit power may be more effectively used toincrease spectral efficiency on some other spatial subchannels.

There is therefore a need in the art for techniques toallocate/reallocate transmit power among the spatial subchannels in aMIMO system if the saturation spectral efficiency has been reached by atleast one of the subchannels.

SUMMARY

Aspects of the invention provide techniques to allocate the totaltransmit power to the transmission channels in a multi-channelcommunication system such that higher overall system throughput and/orother benefits may be achieved. The transmission channels may correspondto the spatial subchannels of a MIMO system, the frequency subchannelsof an OFDM system, or the spatial subchannels of the frequencysubchannels in a MIMO-OFDM system.

The total transmit power may be initially allocated to the transmissionchannels based on a particular power allocation scheme (e.g., thewater-filling scheme). The initial allocation may result in more powerbeing allocated to some transmission channels than needed to achieve therequired signal-to-noise ratio (SNR) (e.g., the SNR needed to achievethe maximum allowed data rate), which would then result in thesetransmission channels being operated in the saturation region. In suchsituations, the techniques described herein advantageously reallocatethe excess transmit power of transmission channels operated in thesaturation region to other transmission channels operated below thesaturation region. In this way, higher spectral efficiency may beachieved for the “poorer” transmission channels without sacrificing theperformance of the “better” transmission channels.

In a specific embodiment, a method is provided for allocating transmitpower to a number of transmission channels in a multi-channelcommunication system. Initially, a set of one or more transmissionchannels to be allocated transmit power is defined. The total transmitpower available to allocate to the transmission channels in the set isdetermined and then allocated to these transmission channels based on aparticular allocation scheme (e.g., the water-filling scheme).Transmission channels operated in the saturation region as a result ofthe allocated transmit powers are then identified. Each suchtransmission channel is allocated a revised amount of transmit power(e.g., the minimum amount needed to achieved the required SNR). Thetotal excess transmit power of all transmission channels reallocatedwith revised transmit powers is then determined.

The above steps may be performed one or more times. The set oftransmission channels for the first iteration includes all transmissionchannels to be allocated transmit power and, for each subsequentiteration, includes only the transmission channels not in the saturationregion. Also, the total transmit power available for each subsequentiteration includes the total excess transmit power determined in thecurrent iteration.

Various aspects and embodiments of the invention are described infurther detail below. The invention further provides methods,processors, transmitter units, receiver units, base stations, terminals,systems, and other apparatuses and elements that implement variousaspects, embodiments, and features of the invention, as described infurther detail below.

BRIEF DESCRIPTION OF THE DRAWINGS

The features, nature, and advantages of the present invention willbecome more apparent from the detailed description set forth below whentaken in conjunction with the drawings in which like referencecharacters identify correspondingly throughout and wherein:

FIG. 1 is a flow diagram of an embodiment of a process for allocatingthe total transmit power among the eigenmodes in a MIMO system usingpower reallocation;

FIG. 2 is a flow diagram of an embodiment of a process for allocatingthe total transmit power among the transmission channels in amulti-channel communication system using power reallocation;

FIG. 3 is a flow diagram of an embodiment of a process for allocatingthe total transmit power among the eigenmodes in a MIMO system thatsupports a set of discrete data rates;

FIG. 4A shows two plots for spectral efficiency versus effective SNR.

FIGS. 4B and 4C show plots of spectral efficiency versus effective SNRfor a communication system that supports a set of discrete data rates;

FIG. 5 is a flow diagram of an embodiment of a process for allocatingthe total available transmit power to a set of eigenmodes based on thewater-filling scheme;

FIGS. 6A and 6B graphically illustrate the allocation of the totaltransmit power to the eigenmodes based on the water-filling scheme; and

FIG. 7 is a block diagram of an embodiment of a transmitter system and areceiver system; and

DETAILED DESCRIPTION

The techniques described herein for allocating/reallocating transmitpower to transmission channels may be used for various multi-channelcommunication systems. Such multi-channel communication systems includemultiple-input, multiple-output (MIMO) communication systems, orthogonalfrequency division multiplexing (OFDM) communication systems, MIMOsystems that utilize OFDM (i.e., MIMO-OFDM systems), and others. Themulti-channel communication systems may also implement code divisionmultiple access (CDMA), time division multiple access (TDMA), frequencydivision multiple access (FDMA), or some other multiple accesstechniques. Multiple access communication systems can support concurrentcommunication with a number of terminals (i.e., users). For clarity,certain aspects and embodiments of the invention are describedspecifically for a MIMO system such as a multiple-antenna wirelesscommunication system.

A MIMO system employs multiple (N_(T)) transmit antennas and multiple(N_(R)) receive antennas for data transmission. A MIMO channel formed bythe N_(T) transmit and N_(R) receive antennas may be decomposed intoN_(S) independent channels, with N_(S)≦min {N_(T), N_(R)}. Each of theN_(S) independent channels is also referred to as a spatial subchannel(or a transmission channel) of the MIMO channel. The number of spatialsubchannels is determined by the number of eigenmodes for the MIMOchannel, which in turn is dependent on a channel response matrix, H,that describes the response between the N_(T) transmit and N_(R) receiveantennas.

The elements of the channel response matrix, H, are composed ofindependent Gaussian random variables, as follows: $\begin{matrix}{{\underset{\_}{H} = \begin{bmatrix}h_{1,1} & h_{1,2} & \cdots & h_{1,N_{T}} \\h_{2,1} & h_{2,2} & \cdots & h_{2,N_{T}} \\\vdots & \vdots & \quad & \vdots \\h_{N_{R},1} & h_{N_{R},2} & \cdots & h_{N_{R},N_{T}}\end{bmatrix}},} & {{Eq}\quad(1)}\end{matrix}$where h_(i,j) is the coupling (i.e., the complex gain) between the j-thtransmit antenna and the i-th receive antenna. The model for the MIMOsystem may be expressed as:y = Hx + n ,   Eq (2)where

-   -   y is the received vector, i.e., y=[y₁ y₂ . . . y_(N) _(R) ]^(T),        where {y_(i)} is the entry received on the i-th received antenna        and iε{1, . . . , N_(R)};    -   x is the transmitted vector, i.e., x=[x₁ x₂ . . . x_(N) _(T)        ]^(T), where {x_(j)} is the entry transmitted from the j-th        transmit antenna and jε{1, . . . , N_(T)};    -   H is the channel response matrix for the MIMO channel;    -   n is the additive white Gaussian noise (AWGN) with a mean vector        of 0 and a covariance matrix of Λ _(n)=σ² I, where 0 is a vector        of zeros, I is the identity matrix with ones along the diagonal        and zeros everywhere else, and σ² is the variance of the noise;        and

[.]^(T) denotes the transpose of [.].

For simplicity, the MIMO channel is assumed to be a flat-fading,narrowband channel. In this case, the elements of the channel responsematrix, H, are scalars, and the coupling, h_(i,j), between eachtransmit-receive antenna pair can be represented by a single scalarvalue. However, the power allocation/reallocation techniques describedherein may also be applied to a frequency selective channel havingdifferent channel gains at different frequencies. In such a frequencyselective channel, the operating bandwidth may be divided into a numberof (equal or unequal) frequency bands such that each band may beconsidered as a flat-fading channel. The response of the individualbands may then be considered in the allocation/reallocation of the totaltransmit power.

Due to scattering in the propagation environment, N_(T) data streamstransmitted from the N_(T) transmit antennas interfere with each otherat the receiver. One technique for eliminating or reducing thisinterference is to “diagonalize” the MIMO channel such that these datastreams are effectively transmitted on orthogonal spatial subchannels.One technique for diagonalizing the MIMO channel is to perform singularvalue decomposition on the channel response matrix, H, which can beexpressed as:H =UDV ^(H) ,   Eq (3)where

-   -   U is an N_(R)×N_(R) unitary matrix (i.e., U ^(H) U=I);    -   D is an N_(R)×N_(T) matrix;    -   V is an N_(T)×N_(T) unitary matrix; and    -   “^(H)”, denotes the complex transpose of a matrix.

The diagonal entries of matrix D are the square roots of the eigenvaluesof G=H ^(H) H, denoted by λ_(i) and iε{1, . . . , N_(S)}, whereN_(S)≦min{N_(T), N_(R)} is the number of resolvable data streams. Allnon-diagonal entries of D are zero.

The diagonal matrix D thus contains non-negative real values along thediagonal and zeros elsewhere, where the non-negative real values ared_(i)=√{square root over (λ_(i))}. The d_(i) are referred to as thesingular values of the channel response matrix, H. The singular valuedecomposition is a matrix operation known in the art and described invarious references. One such reference is a book by Gilbert Strangentitled “Linear Algebra and Its Applications,” Second Edition, AcademicPress, 1980, which is incorporated herein by reference.

The singular value decomposition decomposes the channel response matrix,H, into two unitary matrices, U and V, and the diagonal matrix, D.Matrix D is descriptive of the eigenmodes of the MIMO channel, whichcorrespond to the spatial subchannels. The unitary matrices, U and V,include “steering” vectors for the receiver and transmitter,respectively, which may be used to diagonalize the MIMO channel.Specifically, to diagonalize the MIMO channel, a signal vector, s, maybe pre-multiplied with the matrix, V, and the resultant vector, x=Vs, istransmitted over the MIMO channel. At the receiver, the received vector,y=Hx+n, may be pre-multiplied with the matrix, U ^(H), to obtain arecovered vector, r, as follows: $\begin{matrix}{\begin{matrix}{\underset{\_}{r} = {{{\underset{\_}{U}}^{H}\underset{\_}{HVs}} + {{\underset{\_}{U}}^{H}\underset{\_}{n}}}} \\{= {\underset{\_}{Ds} + \underset{\_}{\hat{n}}}}\end{matrix},} & {{Eq}\quad(4)}\end{matrix}$where {circumflex over (n)} is simply a rotation of n, resulting inadditive white Gaussian noise with the same mean vector and covariancematrix as n.

As shown in equation (4), the pre-multiplication of the signal vector,s, by the matrix V and the pre-multiplication of the received vector, y,by the matrix U ^(H) results in an effective diagonal channel, D, whichis the transfer function between the signal vector, s, and the recoveredvector, r. As a result, the MIMO channel is decomposed into N_(S)independent, non-interfering, orthogonal, and parallel channels. Theseindependent channels are also referred to as the spatial subchannels ofthe MIMO channel. Spatial subchannel i or eigenmode i has a gain that isequal to the eigenvalue, λ_(i), where iεI and set I is defined as I={1,. . . , N_(S)}. Diagonalization of the MIMO channel to obtain N_(S)orthogonal spatial subchannels can be achieved if the transmitter isprovided with an estimate of the channel response matrix, H.

In a typical MIMO system, a peak transmit power of P_(max) may beimposed on each of the N_(T) transmit antennas. In this case, the totaltransmit power, P_(tot), available at the transmitter for all N_(T)transmit antennas may be expressed as:P _(tot) =N _(T) ·P _(max).  Eq (5)The total transmit power, P_(tot), may be allocated to the N_(S)non-zero eigenmodes (i.e., the spatial subchannels) based on variousschemes. If the objective is to maximize capacity (i.e., spectralefficiency), then the total transmit power, P_(tot), may be allocated tothe spatial subchannels by a “water-filling” scheme.

The water-filling scheme is analogous to pouring a fixed amount of waterinto a vessel with an irregular bottom, where each eigenmode correspondsto a point on the bottom of the vessel, and the elevation of the bottomat any given point corresponds to the inverse of the signal-to-noiseratio (SNR) associated with that eigenmode. A low elevation thuscorresponds to a high SNR and, conversely, a high elevation correspondsto a low SNR. The total transmit power, P_(tot), is then “poured” intothe vessel such that the lower points in the vessel (i.e., higher SNRs)are filled first, and the higher points (i.e., lower SNRs) are filledlater. The power distribution is dependent on the total transmit power,P_(tot), and the depth of the vessel over the bottom surface. The watersurface level for the vessel after all of the total transmit power hasbeen poured is constant over all points in the vessel. The points withelevations above the water surface level are not filled (i.e.,eigenmodes with SNRs below a particular threshold are not used). Thewater-filling distribution is described by Robert G. Gallager, in“Information Theory and Reliable Communication,” John Wiley and Sons,1968, which is incorporated herein by reference.

Capacity is defined as the highest spectral efficiency at whichinformation can be communicated with an arbitrarily low probability oferror, and is typically given in unit of bits per second per Hertz(bps/Hz). The capacity for one Gaussian channel with an SNR of γ may beexpressed as:C=log₂(1+γ).  Eq (6)

For a MIMO system with limited total transmit power of P_(tot), thewater-filling scheme can optimally allocate the total transmit power tothe N_(S) spatial subchannels such that capacity is achieved. Thewater-filling scheme distributes the total transmit power, P_(tot), overthe eigenmodes in such a way that the eigenmode with the lowest noisevariance (i.e., the highest SNR) receives the greatest fraction of thetotal power. The amount of power allocated to eigenmode i as a result ofwater filling is denoted by P_(i), for iεI, where $\begin{matrix}{P_{tot} = {\sum\limits_{i \in I}{P_{i}.}}} & {{Eq}\quad(7)}\end{matrix}$

Based on the allocated transmit power of P_(i) for eigenmode i, for iεI,the effective SNR for eigenmode i, γ_(i), may be expressed as:$\begin{matrix}{{\gamma_{i} = \frac{P_{i} \cdot \lambda_{i}}{\sigma^{2}}},} & {{Eq}\quad(8)}\end{matrix}$where λ₁ is the eigenvalue for eigenmode i and σ² is the noise variancefor the MIMO channel. The capacity for the N_(S) spatial subchannels maythen be expressed as: $\begin{matrix}{C = {\sum\limits_{i = 1}^{N_{S}}{{\log_{2}\left( {1 + \gamma_{i}} \right)}.}}} & {{Eq}\quad(9)}\end{matrix}$

The spectral efficiency of each eigenmode may be determined based on aparticular monotonically increasing function in SNR. One function thatmay be used for spectral efficiency is the capacity function shown inequation (6). In this case, the spectral efficiency for eigemnode i,ρ_(i), may be expressed as:ρ_(i)=log₂(1+γ_(i)).  Eq (10)

FIG. 4A shows two plots for spectral efficiency versus SNR. Plot 412shows spectral efficiency increasing logarithmically with SNR ascomputed based on equation (10). Equation (10) assumes that an increasein SNR results in increasingly higher spectral efficiency. However, in apractical communication system, there may be an upper limit on spectralefficiency, which may be dictated, for example, by the maximum data ratesupported by the system on any given data stream. Plot 414 showsspectral efficiency increasing logarithmically at lower SNRs andsaturating at ρ_(sat), which is the upper limit on spectral efficiency.Saturation occurs when an increase in SNR no longer produces an increasein spectral efficiency. The SNR at which spectral efficiency saturatesis denoted as γ_(sat) (i.e., γ_(sat)⇄ρ_(sat)).

Depending on the total transmit power, P_(tot), the eigenvalues, λ_(i),and the noise variance, σ², the allocation of the total transmit powerby the water-filling scheme may result in some eigenmodes being operatedin the saturation region (i.e., γ_(i)>γ_(sat)) and the remainingeigenmodes being operated below this region (i.e., γ_(i)≦γ_(sat)). Aneigenmode is deemed as being operated in the saturation region if it isallocated more transmit power than necessary to achieve the requiredSNR, which is γ_(sat) if the objective is to achieve the maximumpossible spectral efficiency, ρ_(sat). Although the excess transmitpower increases the effective SNR for the eigenmode, which may thenlower the frame error rate (FER), this type of improvement inperformance is typically not substantial since the system may already beoperating at the target FER or at very low FERs. In this case, theexcess transmit power that brings the effective SNR beyond the requiredSNR is not utilized effectively. Improved system performance may beachieved by utilizing the excess transmit power to increase the overallsystem spectral efficiency.

Similarly, in a power-controlled MIMO system, there may be an upperlimit on the SNR allowed at the receiver (i.e., the effective SNRmentioned above) for each eigenmode, which may also be represented asγ_(sat). In this case, if the transmit power allocated to a giveneigenmode results in an effective SNR greater than γ_(sat), then theexcess transmit power that increases the SNR beyond γ_(sat) cannot beused on that eigenmode because of the imposed upper limit on SNR. Thisexcess transmit power may be more beneficially distributed among theother eigenmodes operating below γ_(sat).

An aspect of the invention provides techniques to allocate/reallocatethe total transmit power to the eigenmodes such that higher overallsystem spectral efficiency and/or other benefits may be achieved. Thetotal transmit power may be initially allocated to the eigenmodes basedon a particular power allocation scheme. The initial allocation mayresult in more power being allocated to some eigenmodes than needed toachieve the required SNR (e.g., the γ_(sat) needed to support thesaturation spectral efficiency, ρ_(sat)), which would then result inthese eigenmodes being operated in the saturation region. In suchsituations, the techniques described herein advantageously reallocatethe excess transmit power of eigenmodes operated in the saturationregion to other eigenmodes operated below the saturation region. In thisway, higher spectral efficiency may be achieved for the “poorer”eigenmodes without sacrificing the performance of the “better”eigenmodes.

FIG. 1 is a flow diagram of an embodiment of a process 100 forallocating the total transmit power among the eigenmodes in the MIMOsystem. This process initially allocates the total transmit power,P_(tot), to the N_(S) eigenmodes based on a particular power allocationscheme (e.g., the water-filling scheme). If any of the eigenmodes isallocated more transmit power then needed to achieve the required SNR(i.e., operated in the saturation region), then the total excesstransmit power for these eigenmodes is determined and reallocated to theother eigenmodes. Since the reallocation of the total excess transmitpower may result in some other eigenmodes being operated in thesaturation region, the process may be performed (or iterated) one ormore times until either (1) no excess transmit power is available forreallocation, or (2) all eigenmodes are in the saturation region.

Initially, the variable n used to denote the iteration number isinitialized to one (i.e., n=1) for the first iteration, at step 112. Theset of all eigenmodes, I(n), to be allocated transmit power for thisiteration is then defined, at step 114. For the first iteration, allN_(S) eigenmodes are considered in the allocation of the total transmitpower, and I(n)={1, . . . , N_(S)}. And for each subsequent iteration,only the eigenmodes operated below the saturation region are consideredin the allocation of the total remaining transmit power, and set I(n)would include less than N_(S) eigenmodes or may even be an empty set.

If set I(n) is empty, as determined at step 116, indicating that thereare no eigenmodes operated below the saturation region to which moretransmit power may be allocated, then the process terminates. Otherwise,if set I(n) is not empty, then the total transmit power, P_(tot)(n),available for allocation for this iteration is determined, at step 118.For the first iteration, the total transmit power, P_(tot)(n), availablefor all N_(T) transmit antennas may be determined as shown in equation(5). This assumes that each transmit antenna will be operated at thepeak transmit power, P_(max). And for each subsequent iteration, thetotal transmit power, P_(tot)(n), available for that iteration may bedetermined as described below.

The total available transmit power, P_(tot)(n), is then allocated to theeigenmodes in set I(n) based on the selected power allocation scheme, atstep 120. Various schemes may be used for power allocation such as, forexample, the water-filling scheme, a uniform allocation scheme thatallocates equal amount of transmit power to all eigenmodes, and possiblyother schemes. The transmit power may also be allocated based on schemesthat may take into consideration other factors such as, for example,fairness, one or more system and/or terminal metrics, and so on.

In an embodiment, the water-filling scheme is used to distribute thetotal available transmit power, P_(tot)(n), to the eigenmodes in setI(n). The result of the water-filling procedure is a specific transmitpower, P_(i)(n), allocated to each eigenmode in set I(n), for iεI(n).The power allocation is dependent on the total available transmit power,P_(tot)(n), and the eigenvalues, λ_(i), for the eigenmodes in set I(n).The effective SNR of each eigenmode in set I(n) may then be determinedas: $\begin{matrix}{{{\gamma_{i}(n)} = \frac{{P_{i}(n)} \cdot \lambda_{i}}{\sigma^{2}}},\quad{{{for}\quad i} \in {{I(n)}.}}} & {{Eq}\quad(11)}\end{matrix}$

A determination is then made whether or not any of the eigenmodes in setI(n) are operated in the saturation region given their allocatedtransmit powers, at step 122. This may be achieved by comparing theeffective SNR, γ_(i)(n), determined for each eigenmode, to thesaturation SNR, γ_(sat). Each eigenmode in I(n) having γ_(i)(n) greaterthan γ_(sat) is deemed as being operated in the saturation region andplaced in a temporary set J, such that γ_(j)(n)>γ_(sat) for jεJ. If noneof the eigenmodes in set I(n) are in the saturation region, which isindicated by an empty set J, then there is no excess transmit power toreallocate, and the process terminates. Otherwise, if set J includes atleast one eigenmode, then the excess transmit power for all eigenmodesin set J is determined and reallocated to other eigenmodes not in thesaturation region, if there are any.

The next iteration to reallocate the excess transmit power begins byincrementing the variable n by one (i.e., n=n+1), at step 124. Eacheigenmode in the saturation region, which is included in set J, is thenallocated the minimum amount of transmit power needed to achieve therequired SNR (e.g., γ_(sat)), at step 126. This transmit power can bedetermined as: $\begin{matrix}{{{P_{j}(n)} = \frac{\gamma_{sat} \cdot \sigma^{2}}{\lambda_{j}}},\quad{{{for}\quad j} \in {J.}}} & {{Eq}\quad(12)}\end{matrix}$

The transmit power saved by allocating each eigenmode in set J with theminimum power to achieve its required SNR is then determined, at step128. The total excess transmit power may then be determined as:$\begin{matrix}{{\Delta\quad{P(n)}} = {\sum\limits_{j \in J}{\left( {{P_{j}\left( {n - 1} \right)} - {P_{j}(n)}} \right).}}} & {{Eq}\quad(13)}\end{matrix}$This total excess transmit power, ΔP(n), may now be reallocated to theeigenmodes that are still operated below the saturation region. Theprocess then returns to step 114.

For the second iteration, the set of eigenmodes, I(n), to be allocatedtransmit power in this iteration is defined, at step 114. Set I(n) maybe defined by removing the eigenmodes in set J (i.e., the eigenmodesthat were in the saturation region) from set I(n−1) defined for theprevious iteration. Set I(n) for the current iteration thus onlyincludes eigenmodes that are currently not in saturation. If the new setI(n) is empty, as determined at step 116, then all eigenmodes areoperated in the saturation region and no further reallocation oftransmit power is needed, and the process terminates. Otherwise, if thenew set I(n) is not empty, then the total transmit power, P_(tot)(n),available for the current iteration may be determined as:$\begin{matrix}{{P_{tot}(n)} = {{\sum\limits_{i \in {I{(n)}}}{P_{i}(n)}} + {\Delta\quad{{P(n)}.}}}} & {{Eq}\quad(14)}\end{matrix}$

The total transmit power, P_(tot)(n), available for the currentiteration is then allocated to the eigenmodes in the new set I(n) basedon the selected power allocation scheme, at step 120.

The process shown in FIG. 1 proceeds until either (1) all of the excesstransmit power has been reallocated to the eigenmodes not in thesaturation region (as determined in step 122, which may occur for lowSNR operating environment), or (2) all eigenmodes are in the saturationregion (as determined in step 116, which may occur for high SNRoperating environment).

In the above description, it is assumed that spectral efficiency is astrictly increasing function of the effective SNR, as shown by equation(10). The transmit power allocation/reallocation techniques describedherein may also be used if spectral efficiency is a non-linear functionof the effective SNR. In such cases, the non-linearity may be taken intoaccount when allocating/reallocating the available transmit power to theeigenmodes.

As noted above, the transmit power allocation/reallocation techniquesdescribed herein may also be used for power control in a wirelesscommunication system. Each eigenmode may be associated with a particularsetpoint, which is the target SNR needed to achieve the desiredperformance. The same or different setpoints may be used for the N_(S)eigenmodes. The total transmit power may then be allocated to theeigenmodes such that the setpoint(s) are achieved for these eigenmodes.The process shown in FIG. 1 may be used to reallocate transmit power tothe eigenmodes, where the required SNR is now the setpoint instead ofγ_(sat). The determination of whether or not a particular eigenmode isoperated in the saturation region may thus be dependent on the specificsetpoint associated with that eigenmode (instead of a common SNR, suchas γ_(sat)).

The transmit power allocation/reallocation techniques described hereinmay also be used for other multi-channel communication systems, such asOFDM systems, MIMO-OFDM systems, and so on.

An OFDM system effectively partitions the system bandwidth into a numberof (N_(F)) frequency subchannels, which are also commonly referred to asfrequency bins or subbands. Each frequency subchannel is associated witha respective subcarrier (or frequency tone) upon which data may bemodulated. At each time slot, which is a particular time interval thatmay be dependent on the bandwidth of a frequency subchannel, amodulation symbol may be transmitted on each of the N_(F) frequencysubchannels. For the OFDM system, each frequency subchannel may bereferred to as a transmission channel, and there are N_(C)=N_(F)transmission channels for the OFDM system.

The frequency subchannels of the OFDM system may experience frequencyselective fading (i.e., different amounts of attenuation for differentfrequency subchannels). The specific response for the frequencysubchannels is dependent on the characteristics (e.g., the fading andmultipath effects) of the propagation path between the transmit andreceive antennas. Consequently, different effective SNRs may be achievedfor different frequency subchannels for a given amount of transmitpower. In this case, the total transmit power may be allocated to theN_(F) frequency subchannels in similar manner as that described abovefor the eigenmodes.

A MIMO-OFDM system includes N_(F) frequency subchannels for each of theNs eigenmodes. Each frequency subchannel of each eigenmode may bereferred to as a transmission channel, and there are N_(C)=N_(F)·N_(S)transmission channels for the MIMO-OFDM system. The frequencysubchannels of each eigenmode in the MIMO-OFDM system may similarlyexperience different channel conditions and may achieve different SNRsfor a given amount of transmit power. In this case, the total transmitpower may also be allocated to the N_(C) transmission channels insimilar manner as that described above for the eigenmodes.

FIG. 2 is a flow diagram of an embodiment of a process 200 forallocating the total transmit power among N_(C) transmission channels ina multi-channel communication system. Process 200 may be used for anymulti-channel communication system, including a MIMO system, an OFDMsystem, a MIMO-OFDM system, and so on. Process 200 initially allocatesthe total transmit power, P_(tot), to the N_(C) transmission channelsbased on a particular power allocation scheme (e.g., the water-fillingscheme). If any of the transmission channels are allocated more transmitpower than needed to achieve the required SNR (i.e., operated in thesaturation region), then the total excess transmit power for thesetransmission channels is determined and reallocated to the othertransmission channels. Again, the transmit power allocation may beperformed (or iterated) one or more times until either (1) no excesstransmit power is available for reallocation, or (2) all transmissionchannels are in the saturation region.

Initially, the variable n used to denote the iteration number isinitialized to one (i.e., n=1) for the first iteration, at step 212. Theset of all transmission channels, I(n), to be allocated transmit powerfor this iteration is then defined, at step 214. For the firstiteration, all N_(C) transmission channels are considered in theallocation of the total transmit power, and I(n)={1, . . . , N_(C)},where N_(C)=N_(S) for a MIMO system, N_(C)=N_(F) for an OFDM system, andN_(C)=N_(F)·N_(S) for a MIMO-OFDM system. And for each subsequentiteration, only transmission channels operated below the saturationregion are considered in the allocation of the total remaining transmitpower. Set I(n) would then include less than N_(C) transmission channelsor may even be an empty set.

If set I(n) is empty, as determined at step 216, indicating that thereare no transmission channels operated below the saturation region towhich more transmit power may be reallocated, then the processterminates. Otherwise, the total transmit power, P_(tot)(n), availablefor allocation for this iteration is determined, at step 218. The totalavailable transmit power, P_(tot)(n), is then allocated to thetransmission channels in set I(n) based on the selected power allocationscheme, at step 220.

A determination is then made whether or not any of the transmissionchannels in set I(n) are operated in the saturation region given theirallocated transmit powers, at step 222. This may be achieved bycomparing the effective SNR, γ_(i)(n), determined for each transmissionchannel in set I(n) to the setpoint applicable to that transmissionchannel. Depending on the system design, one setpoint may be used for(1) all transmission channels, (2) each transmit antenna or eachfrequency subchannel, (3) each transmission channel, or (4) each groupof transmission channels. Each transmission channel having an effectiveSNR greater than the applicable setpoint is deemed to be operated in thesaturation region and placed in set J. If no transmission channels arein the saturation region, as indicated by an empty set J, then there isno excess transmit power to reallocate, and the process terminates.Otherwise, if set J includes at least one transmission channel, then theexcess transmit power of all transmission channels in set J isdetermined and reallocated to other transmission channels, if any, thatare not currently operated in the saturation region.

The next iteration to reallocate the excess transmit power begins byincrementing the variable n by one (i.e., n=n+1), at step 224. Eachtransmission channel in the saturation region is then allocated theminimum amount of transmit power needed to achieve the applicablesetpoint, at step 226. The transmit power saved by allocating eachtransmission channel in set J with the minimum power to achieve itssetpoint is then determined, at step 228. The total excess transmitpower may now be reallocated to transmission channels that are stilloperated below the saturation region. The process then returns to step214.

For the second iteration, the set of transmission channels, I(n), to beallocated transmit power in this iteration is defined to include onlytransmission channels that are currently not in saturation, at step 214.If the new set I(n) is empty, as determined at step 216, then alltransmission channels are operated in the saturation region, no furtherreallocation of transmit power is needed, and the process terminates.Otherwise, if the new set I(n) is not empty, then the total transmitpower, P_(tot)(n), available for the current iteration is determined, atstep 218, and then allocated to the transmission channels in the new setI(n) based on the selected power allocation scheme, at step 220.

The process shown in FIG. 2 proceeds until either (1) all of the excesstransmit power has been reallocated to the transmission channels not inthe saturation region (as determined in step 222), or (2) alltransmission channels are in the saturation region (as determined instep 216).

For a MIMO-OFDM system, all transmission channels (i.e., for both thespatial and frequency dimensions) may be considered for power allocationin each iteration. Alternatively, the power allocation may be performedsuch that the transmission channels for only one dimension areconsidered at any given time. For example, power allocation may beperformed on a per-transmit antenna basis whereby the total transmitpower, P_(max), for each transmit antenna is allocated to the frequencysubchannels of that transmit antenna.

The techniques described herein may also be used to allocate/reallocatetransmit power to groups of transmission channels. Each group mayinclude any number of transmission channels and may be associated with arespective setpoint. Each group may include, for example, thetransmission channels to be used for an independent data stream, whichmay be associated with a particular data rate and a particular codingand modulation scheme. For a multiple-access communication system, eachgroup may be associated with the transmission channels to be assigned toa different receiver.

In the above description for the MIMO system, singular valuedecomposition is used to diagonalize the MIMO channel. In otherembodiments, the receiver may provide an indication of the quality ofeach transmission channel that may be used for data transmission. Theinformation reported by the receiver may be in the form of an estimatedSNR, a supported data rate, and so on. The transmitter can then allocatetransmit power to the transmission channels based on the reportedinformation to achieve better utilization of the available transmitpower. For example, if the estimated SNR for a given transmissionchannel is higher than needed to achieve a designated data rate, or ifthe data rate reported as being supported by a given transmissionchannel is greater than the system's maximum data rate, then lesstransmit power may be allocated for the transmission channel. Thespecific amount of transmit power to be allocated may be determinedbased on the reported information (e.g., the estimated SNR or supporteddata rate).

A specific numerical example is described below to illustrate thetechniques for allocating/reallocating the total transmit power amongeigenmodes. For this example, the peak transmit power for each transmitantenna is normalized so that P_(max)=1, and the variance of the noiseis set so that the SNR at each receiver, assuming no other channeldegradation, is γ_(rx)=15 dB. This then results in a noise variance ofσ²=10^(−15/10)=0.0316. The following parameters are also assumed:N_(S)=N_(T)=N_(R)=4,λ₁=2.4, λ₂=1.0, λ₃=0.4, and λ₄=0.2, andγ_(sat)|_(dB)=15 dB→γ_(sat)=31.62.

At initialization (i.e., n=1 in FIG. 1), the set of eigenmodes to beallocated transmit power is defined to be I(1)={1, 2, 3, 4} (step 114)and the total transmit power is P_(tot)(n)=4·1=4 (step 118). For thefirst iteration, the water-filling power allocation (step 120) resultsin the following powers being assigned to the eigenmodes in set I(1):P₁(1)=1.06, P₂(1)=1.04, P₃(1)=0.99, and P₄(1)=0.91.

The effective SNRs for the eigenmodes in set I(1), calculated usingequation (11), are determined to be:γ₁(1)=80.25, γ₂(1)=32.85, γ₃(1)=12.54, and γ₄(1)=5.77.Since γ_(sat)=31.62, it can be observed that eigenmodes 1 and 2 areoperated in the saturation region. Thus, the set of eigenmodes in thesaturation region is defined as J={1, 2}.

Since set J is not empty (step 122), transmit power reallocation isperformed. This is achieved by first incrementing the index n to n=2(step 124). The eigenmodes in the saturation region are then allocatedthe minimum amount of transmit power to achieve λ_(sat). The newtransmit power allocation for eigenmodes 1 and 2 in set J can bedetermined using equation (12) (step 126), as follows:${P_{1}(2)} = {\frac{31.62 \times 0.0316}{2.4} = {{0.42\quad{and}\quad{P_{2}(2)}} = {\frac{31.62 \times 0.0316}{1.0} = {1.00.}}}}$The total excess transmit power for eigenmodes 1 and 2 is thendetermined using equation (13) (step 128), as follows:ΔP=(1.06−0.42)+(1.04−1.00)=0.68.

For the second iteration (n=2), the set of eigenmodes I(2) to beallocated transmit power is redefined (step 114) to include only thosethat are currently not in the saturation region, which is I(2)={3, 4}.The total transmit power available for this iteration is then determinedusing equation (14) (step 118), as follows:P _(tot)(2)=0.99+0.91+0.68=2.58.The total available transmit power, P_(tot)(2), is then allocated to theeigenmodes in set I(2). For the second iteration, the water-fillingpower allocation (step 120) results in the following powers beingassigned to the eigenmodes in set I(2):P₃(2)=1.33 and P₄(2)=1.25.

The effective SNRs for eigenmodes 3 and 4 are then determined to be:γ₃(2)=16.84 and γ₄(2)=7.92.Since γ_(sat)=31.62, it can be observed that none of the eigenmodes areoperated in the saturation region, and the transmit power allocationprocess terminates. The final transmit power allocation for eigenmodes 1through 4 is as follows:P₁=0.42, P₂=1.00, P₃=1.33, and P₄=1.25,and the effective SNRs are:γ₁=31.62, γ₂=31.62, γ₃=16.84, and γ₄=7.92.

After the total transmit power has been allocated to the eigenmodes, thespectral efficiency for each eigenmode in set I(1)={1, 2, 3, 4} can bedetermined using equation (10). The total spectral efficiency, ρ_(tot),may then be obtained by summing the spectral efficiency achieved by eachof the eigenmodes.

It can be shown that a gain of 2 to 5 dB may be achieved at intermediateSNRs by reallocating the excess transmit power of eigenmodes in thesaturation region to other eigenmodes not in the saturation region. Atlow SNRs, the eigenmodes do not enter the saturation region, and thereis little or no transmit power to reallocate. And at high SNRs, most orall of the eigenmodes may be operated in the saturation region, and thetransmit power reallocation may be used to reduce the amount ofinterference, which may improve the performance of neighboring cells.

Power Allocation/Reallocation for Discrete Data Rates

In the above description, it is assumed that the spectral efficiency, ρ,is a continuous function of the effective SNR, γ, as shown in equation(10). Furthermore, the system described above allows the spectralefficiency to be any real value that does not exceed the saturationpoint, ρ_(sat). A typical communication system, however, may onlysupport a set of discrete data rates for each spatial subchannel, andthe data rate sets may or may not be identical for the subchannels.

FIG. 4B shows a plot of spectral efficiency versus effective SNR for acertain eigenmode in a communication system that supports a set ofdiscrete data rates for each eigenmode. Each set of data rates may beconverted to a set of discrete spectral efficiencies and is furtherassociated with a set of discrete effective SNRs needed to achieve atarget frame error rate (FER) for a data transmission on the spatialsubchannel.

In FIG. 4B, the discrete spectral efficiencies are labeled as ρ_(i)(d)on the vertical axis and occur at the corresponding SNRs of γ_(i)(d),where i (iεI) refers to eigenmode i and d (1≦d≦D_(i)) is used toenumerate through the Di discrete data rates associated with eigenmodei. The highest spectral efficiency for eigenmode i occurs at d=D_(i) andcorresponds to the saturation spectral efficiency occurring at thesaturation SNR, γ_(sat)(i)=γ_(i)(D_(i)). The spectral efficiencyfunction for this system is shown by plot 422 (the thick solid line).The discrete operating points at ((γ_(i)(d), ρ_(i)(d)) corresponding tothe minimum SNR necessary to achieve a certain spectral efficiency areshown by the solid circles 424. As seen from the spectral efficiencyfunction in FIG. 4B, an increase in SNR may not offer an improvement inspectral efficiency. Therefore, allocating more transmit power thannecessary to achieve the target FER at the operating spectral efficiencywould result in an ineffective use of the additional transmit power.

The excess power allocation/reallocation techniques described above maybe used for systems with discrete data rates and setpoints.

FIG. 3 is a flow diagram of an embodiment of a process 300 forallocating the total transmit power among the eigenmodes in a MIMOsystem that supports a set of discrete data rates. Initially, the totaltransmit power, P_(tot), is allocated to the N_(S) eigenmodes based on aparticular power allocation scheme (e.g., the water-filling scheme), atstep 312. At the end of the initial transmit power allocation, eacheigenmode is allocated transmit power of P_(i), for iεI, where the powerallocated to a given eigenmode may be zero. If the effective SNR of aneigenmode does not fall on one of the discrete operating points, thensome transmit power allocated to this eigenmode is used inefficientlyand power control may be employed.

The eigenmodes whose effective SNRs do not fall on the set of discreteoperating points are placed in set K, at step 314. If set K is empty, asdetermined in step 316, then the process terminates. Otherwise, eacheigenmode in set K is allocated the minimum amount of transmit powernecessary to meet the current spectral efficiency contribution of thateigenmode, at step 318. This is achieved by backing off (or reducing)the transmit power allocated to each eigenmode in K so that theeigenmode is now operating at the discrete operating point.

FIG. 4B also shows an example system whereby the initial operatingpoints of the three eigenmodes, shown in by dashed lines 426 a through426 c, do not lie on the discrete operating points. The transmit powerfor each of these eigenmodes is reduced by a backed-off amount, BO_(k),for kεK, so that the eigenmode is operating at a lower transmit powerwithout incurring a loss in spectral efficiency. The transmit power,{circumflex over (P)}_(k), required to operate at the discrete operatingpoint, d, for eigenmode k may be expressed as: $\begin{matrix}{{{\hat{P}}_{k} = \frac{{\gamma_{k}(d)} \cdot \sigma^{2}}{\lambda_{k}}},} & {{Eq}\quad(15)}\end{matrix}$where the variable k, for kεK⊂I, refers to each eigenmode in set K, andγ_(k)(d) is the discrete operating point that corresponds to the currentspectral efficiency, ρ_(k)(d), on eigenmode k.

The excess transmit power obtained by decreasing the transmit powerallocated to the eigenmodes in set K is then determined, at step 320, asfollows: $\begin{matrix}{{{\Delta\quad\hat{P}} = {\sum\limits_{k \in K}\left( {P_{k} - {\hat{P}}_{k}} \right)}},} & {{Eq}\quad(16)}\end{matrix}$where P_(k) refers to the initial transmit power allocated to eigenmodek in step 312. Because the excess power can only be reallocated amongthe eigenmodes operating below their respective saturation regions,those eigenmodes from the complete set of eigenmodes, I, whose new (orunchanged) effective SNRs are below their saturation points, γ_(sat)(i),are denoted by the index j and placed into set J, at step 322. If set Jis empty, as determined at step 324, then the process terminates. Set Jthus contains all eigenmodes in set I that are operating below theirrespective saturation (not operating) point once the new powers havebeen applied to the eigenmodes in set K.

Otherwise, the excess transmit power, Δ{circumflex over (P)}, determinedin step 320 is reallocated among the eigenmodes in set J in variousdifferent combinations (e.g., in all possible combinations), at step326. This can be performed based on knowledge of the spectral efficiencyas a function of the effective SNR for each eigenmode (e.g., as shown byplot 422 in FIG. 4B). To facilitate the evaluation in step 326, a tableof incremental SNRs, Δγ_(j)(d), and the corresponding gains in spectralefficiency, Δρ_(j)(d), may be determined for each operating point d ofeach eigenmode j in set J.

The incremental SNR, Δγ_(j)(d), is defined as:Δγ_(j)(d)=γ_(j)(d+1)−γ_(j)(d),  Eq (17)and is the minimum amount of SNR needed to move eigenmode j from thespectral efficiency at the current operating point, d, up to theoperating point of the next higher spectral efficiency, d+1. Thecorresponding gain in spectral efficiency, Δρ_(j)(d), is given by:Δρ_(j)(d)=ρ_(j)(d+1)−ρ_(j)(d),  Eq (18)and is obtained by increasing the SNR from γ_(j)(d) to γ_(j)(d+1).

FIG. 4B illustrates both the incremental SNR and the resulting gain inspectral efficiency for the given spectral efficiency function. Theincremental SNR, Δγ_(j)(d), can be translated to an incremental transmitpower, ΔP_(j)(d), as follows: $\begin{matrix}{{\Delta\quad{P_{j}(d)}} = {\frac{\Delta\quad{{\gamma_{j}(d)} \cdot \sigma^{2}}}{\lambda_{j}}.}} & {{Eq}\quad(19)}\end{matrix}$ΔP_(j)(d) is the incremental power required to achieve the next higherspectral efficiency on eigenmode j from the current operating point, d.

The reallocation of the excess transmit power may be performed so thatthe highest possible gain in spectral efficiency is achieved. This maybe achieved by performing an exhaustive search (or evaluation) of allpossible reallocations of the excess transmit power, Δ{circumflex over(P)}, to all eigenmodes in set J using the incremental transmit powerand the corresponding gain in spectral efficiency obtained fromequations (19) and (18), respectively, at step 328. Finally, the excesstransmit power is distributed according to the reallocation that yieldsthe highest gain in spectral efficiency, at step 330. The process thenterminates.

Various other schemes may also be used to reallocate the excess transmitpower to the eigenmodes in set J. In one scheme, the excess transmitpower is reallocated to one eigenmode at a time starting with the besteigenmode. For example, some excess transmit power may be reallocated tothe highest eigenmode in set J (e.g., just enough power to move thiseigenmode to the next higher spectral efficiency level). Some remainingexcess transmit power may then be reallocated to the next highesteigenmode in set J, and the process can continue in this manner untilall excess transmit power has been reallocated. In another scheme, allpower reallocations that would achieve a jump to the next higherspectral efficiency for each eigenmode in set J are initiallydetermined, and the reallocation that achieves the highest spectralefficiency gain (or uses the least amount of incremental transmit powerif the gains in spectral efficiency are the same over all theeigenmodes) is selected. Other schemes may also be used and are withinthe scope of the invention.

A specific numerical example is described below to illustrate thetechniques for allocating/reallocating the total transmit power amongeigenmodes for a system that supports a set of discrete data rates. Forthis example, the peak transmit power for each transmit antenna isnormalized so that P_(max)=1, and the variance of the noise is set sothat the SNR at each receiver, assuming no other channel degradation, isγ_(rx)=10 dB. This then results in a noise variance ofσ²=10^(−10/10)=0.10. The following parameters are also assumed:N_(S)=N_(T)=N_(R)=3, andλ₁=1.7, λ₂=0.9, and λ₃=0.4.

FIG. 4C shows the spectral efficiency versus effective SNR for the aboveexample system. The same set of discrete data rates is assumed to applyfor all eigenmodes and is associated with the spectral efficiencyfunction shown by plot 432. The saturation SNR for each eigenmode isthus, γ_(sat)(i)|_(dB)=12 dB, ∀iεI.

The total transmit power available at the transmitter is P_(tot)=3·1=3.The water-filling power allocation (step 312) results in the followingpowers being assigned to the three eigenmodes:P ₁(1)=1.08, P₂(1)=1.03, and P₃(1)=0.89.The effective SNRs for the eigenmodes, calculated using equation (11),are determined to be:γ₁(1)=18.38, γ₂(1)=9.26, and γ₃(1)=3.56

The locations of the effective SNRs of the three eigenmodes on thespectral efficiency function is shown by diamonds 438 a through 438 c inFIG. 4C. It can be seen that all three eigenmodes do not lie on thediscrete operating points shown by solid circles 434. Thus, set K isdetermined to be K={1, 2, 3} (step 314). Since set K is not empty, theminimum transmit power for each eigenmode that still results in thecurrent spectral efficiency value of that eigenmode is determined (step318). For this example, the transmit powers of the eigenmodes are backedoff so that the effective SNRs are 12 dB, 9 dB, and 3 dB for the first,second, and third eigenmode, respectively.

Using equation (15), the new transmit powers for the three eigenmodesare determined to be: $\begin{matrix}{{{\hat{P}}_{1} = {\frac{10^{({12/10})} \times 0.1}{1.7} = 0.93}},} \\{{{{\hat{P}}_{2} = {\frac{10^{({9/10})} \times 0.1}{0.9} = 0.88}},\quad{and}}\quad} \\{{\hat{P}}_{3} = {\frac{10^{({3/10})} \times 0.1}{0.4} = {0.50.}}}\end{matrix}$

The new transmit power allocations push the operating points of thethree eigenmodes to the discrete operating points. Next, the excesstransmit power is determined by equation (16) to beΔ{circumflex over (P)}=(1.08−0.93)+(1.03−0.88)+(0.89−0.50)=0.69.

Since the first eigenmode is already at its saturation point, no moretransmit power is reallocated to this eigenmode. The excess transmitpower can be reallocated to eigenmodes two and three, and set J is equalto J={2, 3}.

Table 1 lists the incremental SNR, Δγ_(j)(d), for each operating point,d, and each eigenmode, for jεJ. Because the discrete data rates are thesame for all eigenmodes in this example, the subscript j is dropped andthe incremental SNR is expressed as Δγ(d). The incremental transmitpower, ΔP_(j)(d), on eigenmode j is a function of the eigenvalue oneigenmode j, λ_(j). The ΔP_(j)(d)s are shown for each eigenmode, forjεJ, and for each operating point, d, as calculated using equation (19).Finally, the last column lists the incremental gain in spectralefficiency, Δρ_(j)(d), which remains constant at 0.5 bps/Hz for alloperating points, as shown in FIG. 4C. TABLE 1 d Δγ(d)(dB) ΔP₂(d) ΔP₃(d)Δρ(d) 1 3 0.22 0.50 0.5 2 2 0.18 0.40 0.5 3 1.5 0.16 0.35 0.5 4 2.5 0.200.44 0.5 5 3 0.22 0.5 0.5 6 inf inf inf 0

The next step is then to determine all possible reallocations of theexcess transmit power, Δ{circumflex over (P)}=0.69. Because the secondand third eigenmodes are operating at d=5 and d=2, respectively, thereis only one valid allocation of the excess power, which is to reallocateΔP₂(d)=0.22 more transmit power to the second eigenmode and ΔP₃(d)=0.40more transmit power to the third eigenmode. This power reallocation willresult in an increase of 1 bps/Hz in spectral efficiency, and the amountof unused transmit power is Δ{circumflex over(P)}_(u)=0.69−0.22−0.40=0.7.

As noted above, the techniques described herein forallocating/reallocating transmit power to transmission channels may beused for various multi-channel communication systems, including MIMOsystems, OFDM systems, MIMO-OFDM systems, and so on. These techniquesmay be advantageously used for systems having a saturation spectralefficiency, ρ_(sat), (as illustrated in FIG. 4A) and for systemssupporting one or more sets of discrete data rates for the transmissionchannels (as illustrated in FIG. 4B). The process shown in FIG. 3 may bemodified to allocate/reallocate transmit power to transmission channels(instead of eigenmodes).

Power Allocation/Reallocation for a Specified Spectral Efficiency

The techniques described above may be used to allocate/reallocate thetotal transmit power to maximize spectral efficiency (e.g., to achievethe highest possible overall throughput or aggregate data rate for thetransmission channels). For some communication systems, the aggregatedata rate may be limited or specified. For these systems, the techniquesdescribed above may be modified and used to allocate the minimum amountof transmit power that achieves the specified aggregate data rate.

The allocation of the minimum transmit power that achieves a particularspectral efficiency may be performed in various manners, which may bedependent on the design and capabilities of the communication system.Several possible schemes are provided below.

For a system that supports a set of discrete data rates, the minimumtransmit power allocation for a specified spectral efficiency may beachieved as follows.

-   -   1. Allocate the total transmit power to the transmission        channels, e.g., based on the water-filling scheme.    -   2. Determine a new transmit power for each transmission channel        using the techniques mentioned above such that its operating        point falls on a discrete operating point that achieves the same        spectral efficiency.    -   3. Determine the aggregate spectral efficiency achieved with the        new transmit power allocation. If this spectral efficiency is        higher than the specified spectral efficiency, then proceed to        step 4. Otherwise, the transmit power allocation is finished.    -   4. Determine the “excess” spectral efficiency as the difference        between the achievable spectral efficiency (with the new        transmit power allocation) and the specified spectral        efficiency. The spectral efficiency of the system is then        lowered by this determined difference.    -   5. Form a table of incremental transmit power/incremental        spectral efficiency for each transmission channel, an example of        which is Table 1.    -   6. Search over various possible reductions in transmit power        that will achieve a spectral efficiency reduction less than or        equal to the excess spectral efficiency determined in step 4.    -   7. From step 6, select the transmit power reduction that        maximizes the amount of transmit power saved.

For a system that supports more continuously variable data rates (e.g.,discrete data rates of finer increments), an iterative search may beperformed to determine the minimum transmit power allocation for aspecified spectral efficiency. In particular, after the total transmitpower has been initially allocated (e.g., based on the water-fillingscheme), the excess spectral efficiency may be determined as describedabove. If the excess spectral efficiency exceeds a particular threshold(e.g., a particular percentage over the specified spectral efficiency),then a new transmit power allocation may be determined that reduces theexcess spectral efficiency. This may be achieved by backing off thetotal transmit power (e.g., by some percentage that may be estimatedbased on the percentage of the excess spectral efficiency), andallocating the backed-off transmit power to the transmission channels(e.g., again based on the water-filling scheme). If the spectralefficiency achieved with the backed-off transmit power is less than thespecified spectral efficiency, then the back-off may be reduced, and thenew backed-off transmit power is again allocated to the transmissionchannels. This process can be iterated as many times as needed until thespectral efficiency achieved with a particular backed-off transmit poweris within the acceptable threshold.

Other schemes for determining the minimum transmit power allocation fora specified spectral efficiency may also be implemented, and this iswithin the scope of the invention.

Water-Filling Power Allocation

When full CSI is available at the transmitter, the MIMO channel can bediagonalized into N_(S) orthogonal channels using singular-valuedecomposition, as described above. This technique results in N_(S)non-interfering spatial subchannels, referred to as eigenmodes, with thepower on eigenmode i being equal to the eigenvalue associated with thateigenmode, λ_(i), for iεI={1, 2, . . . , N_(S)}. The performance on eachspatial subchannel is limited by the additive white Gaussian noise(AWGN) of variance σ².

FIG. 5 is a flow diagram of an embodiment of a process 500 forallocating the total available transmit power to a set of eigenmodes.Process 500 is one specific implementation of the water-filling scheme,and may be used for steps 120, 220, and 312 in FIGS. 1, 2, and 3,respectively. The water-filling scheme determines the transmit power,P_(i), for iεI, to be allocated to the eigenmodes in set I given thetotal transmit power, P_(tot), available at the transmitter, theeigenvalues, λ_(i), and the noise variance, σ².

Initially, the variable n used to denote the iteration number is set toone (i.e., n=1), at step 512. For the first iteration, set I(n) isdefined to include all the eigenmodes (i.e., 1≦i≦N_(S)), at step 514.The cardinality (or length) of set I(n), L_(I)(n)=|I(n)|, for thecurrent iteration is then determined, at step 516, which isL_(I)(n)=N_(S) for the first iteration.

The total “effective” power, P_(TOTAL), to be distributed across theeigenmodes in set I(n) is next determined, at step 518. The totaleffective power is defined to be equal to the total transmit power,P_(tot), available at the transmitter plus the sum of the inverse SNRson each eigenmode, as follows: $\begin{matrix}{P_{TOTAL} = {P_{tot} + {\sum\limits_{i \in I}{\frac{\sigma^{2}}{\lambda_{i}}.}}}} & {{Eq}\quad(20)}\end{matrix}$

FIG. 6A graphically illustrates the total effective power for an examplesystem with three eigenmodes. Each eigenmode has an inverse SNR equal toσ²/λ_(i) (assuming a normalized transmit power of 1.0) for i={1, 2, 3}.The total amount of transmit power available at the transmitter isP_(tot)=P₁+P₂+P₃, and is represented by the shaded area in FIG. 6A. Thetotal effective power is represented by the area in the shaded andunshaded regions in FIG. 6A.

The total transmit power is then allocated to the eigenmode in set I(n).The index i used for the eigenmodes is initialized to one (i.e., i=1),at step 520. The amount of transmit power to be allocated to eigenmode iis then determined, at step 522, based on the following: $\begin{matrix}{P_{i} = {\frac{P_{TOTAL}}{L_{I}(n)} - {\frac{\sigma^{2}}{\lambda_{i}}.}}} & {{Eq}\quad(21)}\end{matrix}$

For water-filling, although the bottom of the water level has anirregular surface, the water level at the top remains constant acrossthe vessel. Likewise and as shown in FIG. 6A, after the total transmitpower, P_(tot), is distributed over the eigenmodes, the final powerlevel is constant across all eigenmodes. This final power level isdetermined by dividing P_(TOTAL) by the number of eigenmodes in setI(n), L_(I)(n). The amount of power allocated to eigenmode i is thendetermined by subtracting the inverse SNR of that eigenmode, σ²/λ_(i),from the final power level, P_(TOTAL)/L_(I)(n), as given by equation(21) and shown in FIG. 6A. Each eigenmode in set I(n) is allocatedtransmit power, P_(i), by step 522. Steps 524 and 526 are part of a loopto allocate transmit power to each eigenmode in set I(n).

FIG. 6B shows a situation where the power allocation by thewater-filling scheme results in an eigenmode receiving negative power,which is the case when (P_(TOTAL)/L_(I)(n))<(σ²/λ_(i)). At the end ofthe power allocation, if there are eigenmodes that have receivednegative powers, as determined at step 528, then the process continuesby removing all eigenmodes with negative powers (i.e., P_(i)<0) from setI(n), at step 530, and incrementing n by one (i.e., n=n+1), at step 532.Therefore, on each subsequent iteration, the total transmit power isdivided among the remaining eigenmodes in set I(n). The procedurecontinues until all eigenmodes in set I(n) have been allocated positivepower, as determine in step 528. The eigenmodes not in set I(n) areallocated zero power.

For clarity, the water-filling scheme has been described specificallyfor eigenmodes. In general, the water-filling scheme may be performedfor any type of transmission channels (e.g., spatial subchannels,frequency subchannels, or frequency subchannels of spatial subchannels,depending on the system being implemented). The process shown in FIG. 5may thus be modified to allocate transmit power to transmission channels(instead of eigenmodes).

A specific algorithm for performing the basic water-filling process fora MIMO-OFDM system is described in U.S. patent application Ser. No.09/978,337, entitled “Method and Apparatus for Determining PowerAllocation in a MIMO Communication System,” filed Oct. 15, 2001,assigned to the assignee of the present application and incorporatedherein by reference.

System

FIG. 7 is a block diagram of an embodiment of a transmitter system 710and a receiver system 750, which are capable of implementing variousaspects and embodiments of the invention.

At transmitter system 710, traffic data is provided from a data source712 to a transmit (TX) data processor 714, which formats, codes, andinterleaves the traffic data based on one or more coding schemes toprovide coded data. The coded traffic data may then be multiplexed withpilot data using, e.g., time division multiplex (TDM) or code divisionmultiplex (CDM) in all or a subset of the transmission channels to beused for data transmission. The pilot data is typically a known datapattern processed in a known manner, if at all. The multiplexed pilotand coded traffic data is then modulated (i.e., symbol mapped) based onone or more modulation schemes (e.g., BPSK, QSPK, M-PSK, or M-QAM) toprovide modulation symbols. The data rate, coding, interleaving, andmodulation for each transmission channel or each group of transmissionchannels may be determined by various controls provided by a controller730.

The modulation symbols are then provided to a TX MIMO processor 720 andfurther processed. In a specific embodiment, the processing by TX MIMOprocessor 720 includes (1) decomposing an estimate of the channelresponse matrix, H, to obtain the unitary matrix, V, and the diagonalmatrix, D, (2) pre-multiplying the modulation symbols (i.e., the signalvector s) with the unitary matrix V, and (3) demultiplexing thepre-conditioned symbols (i.e., the transmit vector x) into N_(T) symbolstreams. In another embodiment, the processing by TX MIMO processor 720simply includes demultiplexing the modulation symbols into N_(T) symbolstreams (i.e., no preconditioning of the symbols with the matrix V). TXMIMO processor 720 may further scale each symbol by an appropriateweight determined based on the amount of transmit power allocated to thetransmission channel used for that symbol. The N_(T) (weighted) symbolstreams are then provided to transmitters (TMTR) 722 a through 722 t.

Each transmitter 722 receives and processes a respective symbol stream.For an OFDM system, each transmitter transforms the symbols (e.g., usingthe IFFT) to form OFDM symbols, and may further append a cyclic prefixto each OFDM symbol to form a corresponding transmission symbol. Eachtransmitter also converts the symbol stream into one or more analogsignals and further conditions (e.g., amplifies, filters, and quadraturemodulates) the analog signals to generate a modulated signal suitablefor transmission over the MIMO channel. N_(T) modulated signals fromtransmitters 722 a through 722 t are then transmitted from N_(T)antennas 724 a through 724 t, respectively.

At receiver system 750, the transmitted modulated signals are receivedby N_(R) antennas 752 a through 752 r, and the received signal from eachantenna 752 is provided to a respective receiver (RCVR) 754. Eachreceiver 754 conditions (e.g., filters, amplifies, and downconverts) thereceived signal and digitizes the conditioned signal to provide arespective stream of samples. Each sample stream may further beprocessed (e.g., demodulated with the recovered pilot) to obtain acorresponding stream of received symbols (denoted as y). A RX MIMOprocessor 760 then receives and processes the N_(R) received symbolstreams to provide N_(T) recovered symbol streams. In a specificembodiment, the processing by RX MIMO processor 760 may include (1)decomposing the estimated channel response matrix to obtain the unitarymatrix, U, (2) pre-multiplying the received symbols (i.e., the vector y)with the unitary matrix, U ^(H), to provide the recovered symbols (i.e.,the vector r), and (3) equalizing the recovered symbols to obtainequalized symbols.

A receive (RX) data processor 762 then demodulates, deinterleaves, anddecodes the equalized symbols to recover the transmitted traffic data.The processing by RX MIMO processor 760 and RX data processor 762 iscomplementary to that performed by TX MIMO processor 720 and TX dataprocessor 714, respectively, at transmitter system 710.

RX MIMO processor 760 may further derive an estimate of the channelresponse matrix, H, for the MIMO channel, the SNRs for the transmissionchannels, and so on, and provide these quantities to a controller 770.RX data processor 762 may also provide the status of each received frameor packet, one or more other performance metrics indicative of thedecoded results, and possibly other information. Controller 770 collectschannel state information (CSI), which may comprise all or some of theinformation received from RX MIMO processor 760 and RX data processor762. The CSI is then processed by a TX data processor 778, modulated bya modulator 780, conditioned by transmitters 754 a through 754 r, andtransmitted back to transmitter system 710.

At transmitter system 710, the modulated signals from receiver system750 are received by antennas 724, conditioned by receivers 722,demodulated by a demodulator 740, and processed by a RX data processor742 to recover the CSI reported by the receiver system. The CSI is thenprovided to controller 730 and used to generate various controls for TXdata processor 714 and TX MIMO processor 720.

Controllers 730 and 770 direct the operation at the transmitter andreceiver systems, respectively. Memories 732 and 772 provide storage forprogram codes and data used by controllers 730 and 770, respectively.

To implement the transmit power allocation/reallocation techniquesdescribed above, controller 730 receives the CSI from receiver system750, which may include the channel response matrix or some otherinformation descriptive of the characteristics of the MIMO channel.Controller 730 then allocates the total transmit power to thetransmission channels such that excess transmit power of transmissionchannels operated in the saturation region are reallocated to othertransmission channels not in the saturation region, as described above.The transmit power, P_(i), allocated to each transmission channel maythen determine the data rate and the coding and modulation scheme to beused for that transmission channel.

Various MIMO and OFDM processing techniques for both the transmitter andreceiver systems are described in detail in the following patentapplications, all of which are assigned to the assignee of the presentapplication and incorporated herein by reference:

-   -   U.S. patent application Ser. No. 09/993,087, entitled        “Multiple-Access Multiple-Input Multiple-Output (MIMO)        Communication System,” filed Nov. 6, 2001;    -   U.S. patent application Ser. No. 09/854,235, entitled “Method        and Apparatus for Processing Data in a Multiple-Input        Multiple-Output (MIMO) Communication System Utilizing Channel        State Information,” filed May 11, 2001;    -   U.S. patent application Ser. Nos. 09/826,481 and 09/956,449,        both entitled “Method and Apparatus for Utilizing Channel State        Information in a Wireless Communication System,” respectively        filed Mar. 23, 2001 and Sep. 18, 2001; and    -   U.S. patent application Ser. No. 10/017,308, entitled        “Time-Domain Transmit and Receive Processing with Channel        Eigenmode Decomposition for MIMO Systems,” filed Dec. 7, 2001.

The transmit power allocation/reallocation techniques described hereinmay be implemented by various means. For example, these techniques maybe implemented in hardware, software, or a combination thereof. For ahardware implementation, the elements used to allocate/reallocatetransmit power to transmission channels may be implemented within one ormore application specific integrated circuits (ASICs), digital signalprocessors (DSPs), digital signal processing devices (DSPDs),programmable logic devices (PLDs), field programmable gate arrays(FPGAs), processors, controllers, micro-controllers, microprocessors,other electronic units designed to perform the functions describedherein, or a combination thereof.

For a software implementation, the transmit powerallocation/reallocation may be implemented with modules (e.g.,procedures, functions, and so on) that perform the functions describedherein. The software codes may be stored in a memory unit (e.g., memory732 in FIG. 7) and executed by a processor (e.g., controller 730). Thememory unit may be implemented within the processor or external to theprocessor, in which case it can be communicatively coupled to theprocessor via various means as is known in the art.

Headings are included herein for reference and to aid in locatingcertain sections. These headings are not intended to limit the scope ofthe concepts described therein under, and these concepts may haveapplicability in other sections throughout the entire specification.

The previous description of the disclosed embodiments is provided toenable any person skilled in the art to make or use the presentinvention. Various modifications to these embodiments will be readilyapparent to those skilled in the art, and the generic principles definedherein may be applied to other embodiments without departing from thespirit or scope of the invention. Thus, the present invention is notintended to be limited to the embodiments shown herein but is to beaccorded the widest scope consistent with the principles and novelfeatures disclosed herein.

1. A method for allocating transmit power to a plurality of transmissionchannels in a wireless communication system, comprising: identifying aset of transmission channels to be allocated transmit power; determininga total transmit power available to allocate to the transmissionchannels; allocating the total transmit power to the transmissionchannels in the set based on a particular allocation scheme; determiningan excess spectral efficiency based in part on the transmit powerallocated to the transmission channels; and reallocating one or moretransmission channels with reduced amounts of transmit power to reducethe excess spectral efficiency.
 2. The method of claim 1, furthercomprising: reducing the transmit power allocated to each transmissionchannel to achieve a preferred operating point.
 3. The method of claim1, further comprising: determining incremental changes in spectralefficiency for a plurality of transmit power reductions for thetransmission channels; and selecting a largest transmit power reductionassociated with an incremental spectral efficiency change that is lessthan or equal to the excess spectral efficiency.
 4. The method of claim1, further comprising: determining a backed-off transmit power; andallocating the backed-off transmit power to the transmission channels inthe set.
 5. The method of claim 1, further comprising: performing thedetermining the backed-off transmit power and the allocating thebacked-off transmit power one or more times until the excess spectralefficiency is within a particular threshold.
 6. A controller in awireless communication system, comprising: means for identifying a setof transmission channels to be allocated transmit power; means fordetermining a total transmit power available to allocate to thetransmission channels; means for allocating the total transmit power tothe transmission channels in the set based on a particular allocationscheme; means for determining an excess spectral efficiency based inpart on the transmit power allocated to the transmission channels; andmeans for reallocating one or more transmission channels with reducedamounts of transmit power to reduce the excess spectral efficiency.
 7. Atransmitter unit in a wireless communication system, comprising: atransmit (TX) data processor operative to code data for a plurality oftransmission channels based on one or more coding and modulation schemesto provide a plurality of streams of symbols; a plurality oftransmitters operative to process the plurality of symbol streams toprovide a plurality of modulated signals suitable for transmission overa communication channel; and a controller operative to allocate transmitpower to the plurality of transmission channels by defining a set of oneor more transmission channels to be allocated transmit power,determining a total transmit power available to allocate to thetransmission channels in the set, allocating the total transmit power tothe transmission channels in the set based on a particular allocationscheme, identifying transmission channels in a saturation regionresulting from the allocated transmit power, reallocating eachtransmission channel in the saturation region with a revised amount oftransmit power, determining a total excess transmit power for alltransmission channels reallocated with revised amounts of transmitpower, and performing the defining, determining, allocating,identifying, and reallocating for one or more iterations, wherein theset of transmission channels for a first iteration includes theplurality of transmission channels and for each subsequent iterationincludes transmission channels not in the saturation region, and whereinthe total transmit power available for each subsequent iterationincludes the total excess transmit power determined in a currentiteration.
 8. The transmitter unit of claim 7, wherein the TX dataprocessor is further operative to scale each modulation symbol with aparticular weight determined based on the transmit power allocated tothe transmission channel used for the modulation symbol.
 9. Thetransmitter unit of claim 7, further comprising: a MIMO processoroperative to pre-condition the plurality of symbol streams todiagonalize the plurality of transmission channels.
 10. A base stationcomprising the transmitter unit of claim
 7. 11. A receiver unit in awireless communication system, comprising: a receive (RX) MIMO processoroperative to receive and process a plurality of streams of samples toprovide a plurality of streams of received symbols, and to derivechannel state information (CSI) for a plurality of transmission channelsused for the plurality of received symbol streams; and a RX dataprocessor operative to process the plurality of received symbol streamsin accordance with one or more demodulation and decoding schemes toprovide decoded data, and wherein transmit power for the plurality oftransmission channels is allocated based in part on the CSI byallocating a total available transmit power to the plurality oftransmission channels based on a particular allocation scheme,reallocating each transmission channel in a saturation region with arevised amount of transmit power, and allocating total remainingtransmit power to transmission channels not in the saturation region.12. The receiver unit of claim 11, wherein the RX MIMO processor isfurther operative to pre-condition the plurality of received symbolstreams to diagonalize the plurality of transmission channels.
 13. Thereceiver unit of claim 11, further comprising: a TX data processoroperative to process the CSI for transmission back to a transmitterunit.
 14. A receiver apparatus in a wireless communication system,comprising: means for processing a plurality of streams of samples toprovide a plurality of streams of received symbols, and to derivechannel state information (CSI) for a plurality of transmission channelsused for the plurality of received symbol streams; and means forprocessing the plurality of received symbol streams in accordance withone or more demodulation and decoding schemes to provide decoded data,and wherein transmit power for the plurality of transmission channels isallocated based in part on the CSI by allocating a total availabletransmit power to the plurality of transmission channels based on aparticular allocation scheme, reallocating each transmission channel ina saturation region with a revised amount of transmit power, andallocating total remaining transmit power to transmission channels notin the saturation region.